In this paper, we present a trajectory optimization which tries to exploit as much as possible the problem structure. We advocate the use of representation (REF ) as the model of the non-holonomic vehicle for the simple reason that herein, the curvature constraints are affine functions of control inputs. Thus, it is straightforward to ensure that the output of the trajectory optimization is always kinematically feasible. The central idea of the proposed work hinges on two inter related observations on nonlinear non-convex trajectory optimization. Firstly, the computational performance of such a trajectory optimization depends on how big the trust region is, which is the region where the convex approximation of the problem holds. Secondly, on a related context, the reason why trajectory optimization with linear motion models and circular obstacles are shown to be easily solvable, atleast to local optimality is because they have infinitely big trust region owing to the DC structure of the problem [1]},[2]}, [3]}, [4]}). The proposed trajectory optimization leverages both these observations by using better linearization for non-holonomic motion model and by reformulating collision avoidance between two convex polygons into that between a point and a circle.
